The GOP has obstructed Obama's right to appoint a Supreme Court Justice but it's also waived its right to advise and consent by these ridiculous actions. Obama has an independent constitutional right to fill the vacancy left by Scalia's death. Obama can and should act. The Constitution says the authority is his: according to Article II, when the Senate has gone into recess and the vacancy a president seeks to fill remains, he can appoint someone.
If Donald Trump is allowed to pick a Supreme Court Justice, no one knows the extent of what kind of horrors might befall our country. The Republicans purposely blocked Obama's pick hoping for a GOP victory and they got it. They shouldn't be rewarded for their shady tactics.